Shadowing for discrete approximations of abstract parabolic equations (Q933172)
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scientific article; zbMATH DE number 5302650
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shadowing for discrete approximations of abstract parabolic equations |
scientific article; zbMATH DE number 5302650 |
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Shadowing for discrete approximations of abstract parabolic equations (English)
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21 July 2008
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The paper deals with the analysis of a rather general semi-discretization schemes (i.e. with continuous \(t\)) for the nonlinear problem \[ u^{\prime}(t)=Au(t)+f(u(t)), \quad u(0)=u^{0}, \] where \(A\) is an operator coefficient in a Banach space. The authors prove a shadowing theorem which compares the exact and the semi-discrete solutions.The main assumptions can be verified for operators with compact resolvents and for wide classes of the finite-element as well as finite difference discretizations.
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abstract nonlinear parabolic problem
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Banach space
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finite-element discretization
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finite-difference discretization
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semi-discretization scheme
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shadowing
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